This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
You're on a roll — If two straight lines are perpendicular, their direction vectors are also perpendicular. The dot product of two perpendicular vectors is zero. Step 1: Identify the given direction vectors. Let v_1 = (6, 4) and v_2 = (3, m). Step 2: Set the dot product of the two vectors to zero. The dot product of v_1 = (x_1, y_1) and v_2 = (x_2, y_2) is x_1 x_2 + y_1 y_2. Since the vectors are perpendicular, their dot product is 0: (6)(3) + (4)(m) = 0 Step 3: Solve the equation for m. 18 + 4m = 0 4m = -18 m = (-18)/(4) Step 4: Simplify the value of m. m = (-9)/(2) The final answer is -(9)/(2). What's next?